submitted 4 months ago by Tomorrow_Farewell@hexbear.net to c/chapotraphouse@hexbear.net

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This little guy craves the light of knowledge and wants to know why 0.999... = 1. He wants rigour, but he does accept proofs starting with any sort of premise.

Enlighten him.

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[-] Tomorrow_Farewell@hexbear.net 5 points 4 months ago

Just to be specific, as what a particular sequence converges to depends on the topology of the space where we are looking for a limit of the sequence. Hell, in non-Hausdorff spaces a sequence can have multiple limits (trivial case: anti-discrete space of cardinality greater than 1 will have every sequence converge to every point in it).

[-] EffortPostMcGee@hexbear.net 4 points 4 months ago

Thanks for the clarification! In my mind, I sort of just think "metric first" so the topology induced by that metric is always just assumed, but that's because I don't ever work with non-metrizable spaces.